n∈A(q)

Abstract. An asymptotic formula is given for the number of integers x which are discriminants of cyclic fields of odd prime degree. Let q be afixed odd prime. Letn be a positive integer. It is known thatn is the discriminant of a cyclic field of degree q over Q if and only if n = q2(q−1), (q1 · · · qr)q−1 or q2(q−1)(q1 · · · qr)q−1, where r is a positive integer and q1,..., qr are distinct primes ≡ 1 (mod q), see for example [1], [7]. Let A(q) denote the set of positive integers which are the product of distinct primes ≡ 1 (mod q) including the empty product = 1. Then the number Cq(x) of n x which are discriminants of cyclic fields of degree q is (for large enough x in terms of q) Cq(x) = 1